Given:
The data values are:
22, 14, 24, 20, 36, 28, 43, 35
To find:
The mean absolute deviation of the given numbers.
Solution:
We have,
22, 14, 24, 20, 36, 28, 43, 35
The measure of the given numbers is:
[tex]\overline{x}=\dfrac{\sum_{i=1}^{n} x_i}{n}[/tex]
Where, [tex]x_i[/tex] represents the observations and n is the number of observation.
So, the mean value of the given data set is:
[tex]\overline{x}=\dfrac{22+14+24+20+36+28+43+35}{8}[/tex]
[tex]\overline{x}=\dfrac{222}{8}[/tex]
[tex]\overline{x}=27.75[/tex]
The formula for is mean absolute deviation is:
[tex]M.A.D.=\dfrac{1}{n}\sum_{i=1}^{n}|x_i-\overline{x}|[/tex]
The mean absolute deviation of the given numbers is:
[tex]M.A.D.=\dfrac{1}{8}[|22-27.75|+|14-27.75|+|24-27.75|+|20-27.75|+|36-27.75|+|28-27.75|+|43-27.75|+|35-27.75|][/tex]
[tex]M.A.D.=\dfrac{1}{8}[5.75+13.75+3.75+7.75+8.25+0.25+15.25+7.25][/tex]
[tex]M.A.D.=\dfrac{1}{8}[62][/tex]
[tex]M.A.D.=7.75[/tex]
Therefore, the mean absolute deviation of the given numbers is 7.75.
